Corresponding to optical Fresnel diffraction, we show that the exponential quadratic operator exp{ i[ P2+ Q2+ (PQ+QP)]/2} is actually a generalized single-mode Fresnel operator (GFO) in compact form, where [Q,P]=i . W...Corresponding to optical Fresnel diffraction, we show that the exponential quadratic operator exp{ i[ P2+ Q2+ (PQ+QP)]/2} is actually a generalized single-mode Fresnel operator (GFO) in compact form, where [Q,P]=i . We also demonstrate that exp{i [(Q1+Q2)2+(P1 P2)2]+i [(Q1 Q2)2+(P1+P2)2]+i (Q1P2+Q2P1)} is a two-mode GFO. Their disentangling formula and normal ordering form are derived with the use of technique of integration within an ordered product (IWOP) of operators and the coherent state representation. The squeezed states generated by these two GFOs are obtained.展开更多
基金supported by the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A16)the Specialized Research Fund for the Doctoral Program of Higher Education China (Grant No.20103705110001)
文摘Corresponding to optical Fresnel diffraction, we show that the exponential quadratic operator exp{ i[ P2+ Q2+ (PQ+QP)]/2} is actually a generalized single-mode Fresnel operator (GFO) in compact form, where [Q,P]=i . We also demonstrate that exp{i [(Q1+Q2)2+(P1 P2)2]+i [(Q1 Q2)2+(P1+P2)2]+i (Q1P2+Q2P1)} is a two-mode GFO. Their disentangling formula and normal ordering form are derived with the use of technique of integration within an ordered product (IWOP) of operators and the coherent state representation. The squeezed states generated by these two GFOs are obtained.
